The purpose of this model is to understand how genetic architectures of alternative reproductive tactics impact their maintenance in populations. I’m using an individual-based simulation model with different selection scenarios, types of alternative tactics, and genetic architectures (genome-wide additive genetic variance, supergenes, expression networks).

Overview of the model

Males can be courters or not-courters and parents or not-parents. When the model is run with both traits, this results in four possible morphs: courter/parent, courter/not-parent, not-courter/parent, and not-courter/not-parent. Generations are non-overlapping and there is one reproductive bout per generation. In each generation, the population follows the following timeline:

Fig. 1 Flowchart of simulation

Fig. 1 Flowchart of simulation

each step is explained in further detail below.

1. Choosing a nest

A female samples 50 males and chooses a male to nest with based on his courtship trait. If there are no courtship traits in the model, she chooses based on the male’s parental trait. If she does not encouter an acceptable male, she does not nest. If she encounters multiple equally-acceptable males, she randomly selects one of them.

2. Fertilization

Once a female decides to nest, up to three males can fertilize the nest. Courters and parental males can contribute more sperm than non-courter and non-parental males: \(r_{courter}=r_{parent}=8\) and \(r_{non-courter}=r_{non-parent}=4\). A courter/non-parent has \(r_{non-parent}\) and a non-courter/parent has \(r_{parent}\). The male with whom the female is nesting gets \(r_{parent}/\Sigma{n_{sperm}}\) and additional non-parental males (up to 2) get \((r_{non-parent}*0.5/\Sigma{n_{sperm}})\), where \(\Sigma{n_{sperm}}\) is the total number of sperm contributed by all of the males, weighted by the sperm competition factor (0.5 is the default for all males except the nesting male). So, when a female mates with one courter and two non-parentals, \(\Sigma{n_{sperm}}\) = \(r_{courter}\) + 2\(*\)(0.5\(*\)\(r_{sneaker}\)), where \(r_{courter}\) = 8 and \(r_{sneaker}\) = 4, therefore \(\Sigma{n_{sperm}}\) = 12.

That being said, every time a male mates he uses his sperm, so after one mating where a courter fertilizes 50% of the female’s 4 eggs, he only has 6 sperm for his next mating.

3. Nest Survival

Before the babies can survive, the nest has to survive. This step is only relevant when parental traits are in the model - if only the courtship trait is specified, then all progeny in the nest survive at this point. When males have the parental trait, if the female has given eggs to a non-parental male (because she chose based on courtship traits), then the nest has a 10% chance of surviving. If the female has given eggs to a parental male, the nest has a 90% chance of surviving.

4. Density-dependent survival

Once the identities of the surviving nests are known–along with the identities of the parents, including sneaker parents–the offspring are created in the simulation. The offspring are created to fill the full carrying capacity of the population, with the numbers per nest being equally divided among all surviving offspring. This allows the population to maintain a constant population size (prior to viability selection) while maintaining the relative successes of the given genotypes/morphs.

5. Viability selection

Before becoming adults, the offspring experience viability selection. Courters and parental males are disfavored in viability selection, with a survival probability of 0.9950125. If an individual is both a courter and a parental male, the survival probability is 0.9900498. Non-courters and non-parental males have survival probabilities of 1.

Evaluating equilibrium

After 10000 generations, I begin tracking the change in frequency of the courter and parent traits, and do so for 2000 additional generations. I calculate the variance in the change in frequency over those 2000 generations. I declare an equilibrium (‘stasis’) has been reached if the last change in frequency of both traits is less than the variance in changes in frequency.

Unlinked additive genetic variance

In these cases, the traits are encoded by a number (50) of loci, whose alleles contribute additively to determine the trait value. These alleles are all freely recombining and are not adhered to any physical genomic location (aka this is a classical quantitative genetics approach). The overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

Females choose nests based on whether the male is a courter or not, and they all prefer courters all of the time (the female preference does not have a genetic basis and does not evolve). The only way that non-courters produce offspring is through sneaking, but all males can be sneakers (both courters and non-courters). Because parental care is not incorporated in this model, all nests survive.

With viability selection

Frequency of the courter morph with unlinked additive genetic variances (each color represents a different replicate)

Frequency of the courter morph with unlinked additive genetic variances (each color represents a different replicate)

Of the 20 replicates, 20 reached a steady state by 10000 generations. The different runs all overlap, suggesting that they all converge on the same outcome: all males are courters. This result is also obvious by inspecting a table of courter frequencies and fitnesses in the final generation of the runs.

Frequency of courters in final generation of runs with unlinked additive genetic variances
CourterFreq CourterW NonCourterW
courter_unlinked_1_summary.txt_1 1 2.13675 0
courter_unlinked_1_summary.txt_2 1 2.03666 0
courter_unlinked_1_summary.txt_3 1 2.06186 0
courter_unlinked_1_summary.txt_4 1 2.03252 0
courter_unlinked_2_summary.txt_1 1 2.13675 0
courter_unlinked_2_summary.txt_2 1 2.03666 0
courter_unlinked_2_summary.txt_3 1 2.06186 0
courter_unlinked_2_summary.txt_4 1 2.03252 0
courter_unlinked_3_summary.txt_1 1 2.13675 0
courter_unlinked_3_summary.txt_2 1 2.03666 0
courter_unlinked_3_summary.txt_3 1 2.06186 0
courter_unlinked_3_summary.txt_4 1 2.03252 0
courter_unlinked_4_summary.txt_1 1 1.95303 0
courter_unlinked_4_summary.txt_2 1 2.04723 0
courter_unlinked_4_summary.txt_3 1 2.02857 0
courter_unlinked_4_summary.txt_4 1 2.07708 0
courter_unlinked_5_summary.txt_1 1 1.95303 0
courter_unlinked_5_summary.txt_2 1 2.04723 0
courter_unlinked_5_summary.txt_3 1 2.02857 0
courter_unlinked_5_summary.txt_4 1 2.07708 0

We may also be interested in the evolution of the courter trait values, which reflects the additive effects of all loci.

Evolution of courtship trait with unlinked loci

Evolution of courtship trait with unlinked loci

Without viability selection

Frequency of the courter morph with unlinked additive genetic variances and without viability selection (each color represents a different replicate)

Frequency of the courter morph with unlinked additive genetic variances and without viability selection (each color represents a different replicate)

Of the 20 replicates, 20 reached a steady state by 10000 generations. The different runs all overlap, suggesting that they all converge on the same outcome: all males are courters. This result is also obvious by inspecting a table of courter frequencies and fitnesses in the final generation of the runs.

Frequency of courters in final generation of runs with unlinked additive genetic variances and no viability selection
CourterFreq CourterW NonCourterW
courter_unlinked_novs_1_summary.txt_1 1 2.00401 0
courter_unlinked_novs_1_summary.txt_2 1 2.13220 0
courter_unlinked_novs_1_summary.txt_3 1 2.02020 0
courter_unlinked_novs_1_summary.txt_4 1 2.13220 0
courter_unlinked_novs_2_summary.txt_1 1 2.00401 0
courter_unlinked_novs_2_summary.txt_2 1 2.13220 0
courter_unlinked_novs_2_summary.txt_3 1 2.02020 0
courter_unlinked_novs_2_summary.txt_4 1 2.13220 0
courter_unlinked_novs_3_summary.txt_1 1 2.00401 0
courter_unlinked_novs_3_summary.txt_2 1 2.13220 0
courter_unlinked_novs_3_summary.txt_3 1 2.02020 0
courter_unlinked_novs_3_summary.txt_4 1 2.13220 0
courter_unlinked_novs_4_summary.txt_1 1 2.05339 0
courter_unlinked_novs_4_summary.txt_2 1 2.04918 0
courter_unlinked_novs_4_summary.txt_3 1 1.96078 0
courter_unlinked_novs_4_summary.txt_4 1 1.96850 0
courter_unlinked_novs_5_summary.txt_1 1 2.05339 0
courter_unlinked_novs_5_summary.txt_2 1 2.04918 0
courter_unlinked_novs_5_summary.txt_3 1 1.96078 0
courter_unlinked_novs_5_summary.txt_4 1 1.96850 0

We may also be interested in the evolution of the courter trait values, which reflects the additive effects of all loci.

Evolution of courtship trait with unlinked loci and no viability selection

Evolution of courtship trait with unlinked loci and no viability selection

Parental trait

In this case, there are no courtship traits so females lay eggs in nests randomly. Non-parental males will sneak fertilizations in parental males’ nests. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

With viability selection

Frequency of parent morph with unlinked loci (each color represents a different replicate)

Frequency of parent morph with unlinked loci (each color represents a different replicate)

Again, inference is facilitated by looking at the final frequencies and fitnesses in each replicate:

Frequency of parents in final generation
ParentFreq ParentW NonParentW
parent_unlinked_1_summary.txt_1 1.2478800 1.57238 1.000000
parent_unlinked_1_summary.txt_2 1.2094800 1.65707 0.586667
parent_unlinked_1_summary.txt_3 1.2352000 1.65618 0.903846
parent_unlinked_1_summary.txt_4 1.2041800 1.67285 0.753846
parent_unlinked_2_summary.txt_1 1.2478800 1.57238 1.000000
parent_unlinked_2_summary.txt_2 1.2094800 1.65707 0.586667
parent_unlinked_2_summary.txt_3 1.2352000 1.65618 0.903846
parent_unlinked_2_summary.txt_4 1.2041800 1.67285 0.753846
parent_unlinked_3_summary.txt_1 1.2478800 1.57238 1.000000
parent_unlinked_3_summary.txt_2 1.2094800 1.65707 0.586667
parent_unlinked_3_summary.txt_3 1.2352000 1.65618 0.903846
parent_unlinked_3_summary.txt_4 1.2041800 1.67285 0.753846
parent_unlinked_4_summary.txt_1 0.0426554 1.58862 0.779661
parent_unlinked_4_summary.txt_2 0.0423615 1.66887 1.066670
parent_unlinked_4_summary.txt_3 0.0420778 1.76386 1.114750
parent_unlinked_4_summary.txt_4 0.0413643 1.75878 0.666667
parent_unlinked_5_summary.txt_1 0.0426554 1.58862 0.779661
parent_unlinked_5_summary.txt_2 0.0423615 1.66887 1.066670
parent_unlinked_5_summary.txt_3 0.0420778 1.76386 1.114750
parent_unlinked_5_summary.txt_4 0.0413643 1.75878 0.666667

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Let’s take a look at how the parent trait values evolve

Evolution of parenting trait values with additive genetic variation

Evolution of parenting trait values with additive genetic variation

Without viability selection

Frequency of parent morph with unlinked loci without viability selection (each color represents a different replicate)

Frequency of parent morph with unlinked loci without viability selection (each color represents a different replicate)

Again, inference is facilitated by looking at the final frequencies and fitnesses in each replicate:

Frequency of parents in final generation
ParentFreq ParentW NonParentW
parent_unlinked_novs_1_summary.txt_1 0.821429 1.68798 0.729412
parent_unlinked_novs_1_summary.txt_2 0.897030 1.58278 1.019230
parent_unlinked_novs_1_summary.txt_3 0.897287 1.65443 0.886792
parent_unlinked_novs_1_summary.txt_4 0.889571 1.67126 0.666667
parent_unlinked_novs_2_summary.txt_1 0.821429 1.68798 0.729412
parent_unlinked_novs_2_summary.txt_2 0.897030 1.58278 1.019230
parent_unlinked_novs_2_summary.txt_3 0.897287 1.65443 0.886792
parent_unlinked_novs_2_summary.txt_4 0.889571 1.67126 0.666667
parent_unlinked_novs_3_summary.txt_1 0.821429 1.68798 0.729412
parent_unlinked_novs_3_summary.txt_2 0.897030 1.58278 1.019230
parent_unlinked_novs_3_summary.txt_3 0.897287 1.65443 0.886792
parent_unlinked_novs_3_summary.txt_4 0.889571 1.67126 0.666667
parent_unlinked_novs_4_summary.txt_1 0.878431 1.70089 0.709677
parent_unlinked_novs_4_summary.txt_2 0.876797 1.70726 0.616667
parent_unlinked_novs_4_summary.txt_3 0.855131 1.66824 0.513889
parent_unlinked_novs_4_summary.txt_4 0.859961 1.61239 0.422535
parent_unlinked_novs_5_summary.txt_1 0.878431 1.70089 0.709677
parent_unlinked_novs_5_summary.txt_2 0.876797 1.70726 0.616667
parent_unlinked_novs_5_summary.txt_3 0.855131 1.66824 0.513889
parent_unlinked_novs_5_summary.txt_4 0.859961 1.61239 0.422535

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Let’s take a look at how the parent trait values evolve

Evolution of parenting trait values with additive genetic variation and no viability selection

Evolution of parenting trait values with additive genetic variation and no viability selection

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters and non-parents can reproduce through sneaking.

With viability selection

The different runs have different outcomes.

Let’s look at the morph frequencies for each run.

Frequency of the 4 morphs in each rep with unlinked genetic variation

Frequency of the 4 morphs in each rep with unlinked genetic variation

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentAEmean ParentAEsd ParentFreq ParentW NonParentW CourterThresh CourterAEmean CourterAEsd CourterFreq CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_unlinked_1_summary.txt_1 11999 Pop0 940 471 469 1000 0.890749 0.443737 0.883452 0.0739653 0.000000 0.362595 -0.942183 -0.832353 1.113290 0.556263 0.362595 0 0 0.556263 0.443737 0.000000 NA NA
parent-courter_unlinked_1_summary.txt_2 11999 Pop1 860 433 427 968 0.890749 0.441109 0.883265 0.0738648 0.000000 0.545455 -0.942183 -0.829546 1.111780 0.558891 0.545455 0 0 0.558891 0.441109 0.000000 NA NA
parent-courter_unlinked_1_summary.txt_3 11999 Pop2 936 473 463 1000 0.890749 0.437632 0.881182 0.0748110 0.000000 0.368421 -0.942183 -0.798195 1.126020 0.562368 0.368421 0 0 0.562368 0.437632 0.000000 NA NA
parent-courter_unlinked_1_summary.txt_4 11999 Pop3 942 477 465 1000 0.890749 0.442348 0.881219 0.0751622 0.000000 0.394737 -0.942183 -0.798750 1.131310 0.557652 0.394737 0 0 0.557652 0.442348 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_1 11999 Pop0 940 471 469 1000 0.890749 0.443737 0.883452 0.0739653 0.000000 0.362595 -0.942183 -0.832353 1.113290 0.556263 0.362595 0 0 0.556263 0.443737 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_2 11999 Pop1 860 433 427 968 0.890749 0.441109 0.883265 0.0738648 0.000000 0.545455 -0.942183 -0.829546 1.111780 0.558891 0.545455 0 0 0.558891 0.441109 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_3 11999 Pop2 936 473 463 1000 0.890749 0.437632 0.881182 0.0748110 0.000000 0.368421 -0.942183 -0.798195 1.126020 0.562368 0.368421 0 0 0.562368 0.437632 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_4 11999 Pop3 942 477 465 1000 0.890749 0.442348 0.881219 0.0751622 0.000000 0.394737 -0.942183 -0.798750 1.131310 0.557652 0.394737 0 0 0.557652 0.442348 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_1 11999 Pop0 940 471 469 1000 0.890749 0.443737 0.883452 0.0739653 0.000000 0.362595 -0.942183 -0.832353 1.113290 0.556263 0.362595 0 0 0.556263 0.443737 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_2 11999 Pop1 860 433 427 968 0.890749 0.441109 0.883265 0.0738648 0.000000 0.545455 -0.942183 -0.829546 1.111780 0.558891 0.545455 0 0 0.558891 0.441109 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_3 11999 Pop2 936 473 463 1000 0.890749 0.437632 0.881182 0.0748110 0.000000 0.368421 -0.942183 -0.798195 1.126020 0.562368 0.368421 0 0 0.562368 0.437632 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_4 11999 Pop3 942 477 465 1000 0.890749 0.442348 0.881219 0.0751622 0.000000 0.394737 -0.942183 -0.798750 1.131310 0.557652 0.394737 0 0 0.557652 0.442348 0.000000 NA NA
parent-courter_unlinked_4_summary.txt_1 11999 Pop0 964 465 499 1000 -0.536111 0.565591 -0.587407 0.3684840 1.022810 0.391089 -0.690850 -0.600370 0.649948 0.686022 1.090910 0 0 0.434409 0.313978 0.251613 NA NA
parent-courter_unlinked_4_summary.txt_2 11999 Pop1 962 479 483 1000 -0.536111 0.544885 -0.583240 0.3808790 0.762452 0.435780 -0.690850 -0.607720 0.671811 0.655532 0.936306 0 0 0.455115 0.344468 0.200418 NA NA
parent-courter_unlinked_4_summary.txt_3 11999 Pop2 960 473 487 1000 -0.536111 0.532770 -0.594644 0.3802730 0.777778 0.384615 -0.690850 -0.587605 0.670742 0.670190 0.886435 0 0 0.467230 0.329810 0.202960 NA NA
parent-courter_unlinked_4_summary.txt_4 11999 Pop3 958 479 479 1000 -0.536111 0.582463 -0.564566 0.3733460 0.946237 0.305000 -0.690850 -0.640658 0.658524 0.649269 1.045020 0 0 0.417537 0.350731 0.231733 NA NA
parent-courter_unlinked_5_summary.txt_1 11999 Pop0 964 465 499 1000 -0.536111 0.565591 -0.587407 0.3684840 1.022810 0.391089 -0.690850 -0.600370 0.649948 0.686022 1.090910 0 0 0.434409 0.313978 0.251613 NA NA
parent-courter_unlinked_5_summary.txt_2 11999 Pop1 962 479 483 1000 -0.536111 0.544885 -0.583240 0.3808790 0.762452 0.435780 -0.690850 -0.607720 0.671811 0.655532 0.936306 0 0 0.455115 0.344468 0.200418 NA NA
parent-courter_unlinked_5_summary.txt_3 11999 Pop2 960 473 487 1000 -0.536111 0.532770 -0.594644 0.3802730 0.777778 0.384615 -0.690850 -0.587605 0.670742 0.670190 0.886435 0 0 0.467230 0.329810 0.202960 NA NA
parent-courter_unlinked_5_summary.txt_4 11999 Pop3 958 479 479 1000 -0.536111 0.582463 -0.564566 0.3733460 0.946237 0.305000 -0.690850 -0.640658 0.658524 0.649269 1.045020 0 0 0.417537 0.350731 0.231733 NA NA

Multiple morphs are maintained in 0 of the 20 replicates, and those morphs contain either a parent or a courter.

Evolution of the courter and parenting trait values in each rep with unlinked genetic variation

Evolution of the courter and parenting trait values in each rep with unlinked genetic variation

Without viability selection

The different runs have different outcomes.

Let’s look at the morph frequencies for each run.

Frequency of the 4 morphs in each rep with unlinked genetic variation and no viability selection

Frequency of the 4 morphs in each rep with unlinked genetic variation and no viability selection

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentFreq ParentAEmean ParentAEsd ParentW NonParentW CourterThresh CourterFreq CourterAEmean CourterAEsd CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_unlinked_novs_1_summary.txt_1 11999 Pop0 966 504 462 1000 0.876646 0.906746 1.09688 0.235547 1.82276 1.425530 1.270200 0.906746 2.002970 0.783700 1.822760 1.42553 0.0932540 0.000000 0.000000 0.906746 NA NA
parent-courter_unlinked_novs_1_summary.txt_2 11999 Pop1 951 504 447 1000 0.876646 0.898810 1.09639 0.233716 1.81678 1.470590 1.270200 0.898810 2.001320 0.777608 1.816780 1.47059 0.1011900 0.000000 0.000000 0.898810 NA NA
parent-courter_unlinked_novs_1_summary.txt_3 11999 Pop2 949 472 477 1000 0.876646 0.930085 1.10464 0.237480 1.87699 1.757580 1.270200 0.930085 2.028780 0.790132 1.876990 1.75758 0.0699153 0.000000 0.000000 0.930085 NA NA
parent-courter_unlinked_novs_1_summary.txt_4 11999 Pop3 950 479 471 1000 0.876646 0.908142 1.09918 0.234665 1.92414 1.431820 1.270200 0.908142 2.010620 0.780766 1.924140 1.43182 0.0918580 0.000000 0.000000 0.908142 NA NA
parent-courter_unlinked_novs_2_summary.txt_1 11999 Pop0 966 504 462 1000 0.876646 0.906746 1.09688 0.235547 1.82276 1.425530 1.270200 0.906746 2.002970 0.783700 1.822760 1.42553 0.0932540 0.000000 0.000000 0.906746 NA NA
parent-courter_unlinked_novs_2_summary.txt_2 11999 Pop1 951 504 447 1000 0.876646 0.898810 1.09639 0.233716 1.81678 1.470590 1.270200 0.898810 2.001320 0.777608 1.816780 1.47059 0.1011900 0.000000 0.000000 0.898810 NA NA
parent-courter_unlinked_novs_2_summary.txt_3 11999 Pop2 949 472 477 1000 0.876646 0.930085 1.10464 0.237480 1.87699 1.757580 1.270200 0.930085 2.028780 0.790132 1.876990 1.75758 0.0699153 0.000000 0.000000 0.930085 NA NA
parent-courter_unlinked_novs_2_summary.txt_4 11999 Pop3 950 479 471 1000 0.876646 0.908142 1.09918 0.234665 1.92414 1.431820 1.270200 0.908142 2.010620 0.780766 1.924140 1.43182 0.0918580 0.000000 0.000000 0.908142 NA NA
parent-courter_unlinked_novs_3_summary.txt_1 11999 Pop0 966 504 462 1000 0.876646 0.906746 1.09688 0.235547 1.82276 1.425530 1.270200 0.906746 2.002970 0.783700 1.822760 1.42553 0.0932540 0.000000 0.000000 0.906746 NA NA
parent-courter_unlinked_novs_3_summary.txt_2 11999 Pop1 951 504 447 1000 0.876646 0.898810 1.09639 0.233716 1.81678 1.470590 1.270200 0.898810 2.001320 0.777608 1.816780 1.47059 0.1011900 0.000000 0.000000 0.898810 NA NA
parent-courter_unlinked_novs_3_summary.txt_3 11999 Pop2 949 472 477 1000 0.876646 0.930085 1.10464 0.237480 1.87699 1.757580 1.270200 0.930085 2.028780 0.790132 1.876990 1.75758 0.0699153 0.000000 0.000000 0.930085 NA NA
parent-courter_unlinked_novs_3_summary.txt_4 11999 Pop3 950 479 471 1000 0.876646 0.908142 1.09918 0.234665 1.92414 1.431820 1.270200 0.908142 2.010620 0.780766 1.924140 1.43182 0.0918580 0.000000 0.000000 0.908142 NA NA
parent-courter_unlinked_novs_4_summary.txt_1 11999 Pop0 1000 514 486 1000 1.188380 0.461089 1.07559 1.222950 0.00000 0.339350 0.344879 0.538911 0.373095 0.305945 0.339350 0.00000 0.0000000 0.538911 0.461089 0.000000 NA NA
parent-courter_unlinked_novs_4_summary.txt_2 11999 Pop1 1000 519 481 1000 1.188380 0.452794 1.07010 1.230870 0.00000 0.390845 0.344879 0.547206 0.374467 0.307926 0.390845 0.00000 0.0000000 0.547206 0.452794 0.000000 NA NA
parent-courter_unlinked_novs_4_summary.txt_3 11999 Pop2 1000 533 467 1000 1.188380 0.465291 1.07074 1.214330 0.00000 0.403509 0.344879 0.534709 0.374307 0.303788 0.403509 0.00000 0.0000000 0.534709 0.465291 0.000000 NA NA
parent-courter_unlinked_novs_4_summary.txt_4 11999 Pop3 1000 514 486 1000 1.188380 0.463035 1.09061 1.229310 0.00000 0.489130 0.344879 0.536965 0.369337 0.307536 0.489130 0.00000 0.0000000 0.536965 0.463035 0.000000 NA NA
parent-courter_unlinked_novs_5_summary.txt_1 11999 Pop0 1000 514 486 1000 1.188380 0.461089 1.07559 1.222950 0.00000 0.339350 0.344879 0.538911 0.373095 0.305945 0.339350 0.00000 0.0000000 0.538911 0.461089 0.000000 NA NA
parent-courter_unlinked_novs_5_summary.txt_2 11999 Pop1 1000 519 481 1000 1.188380 0.452794 1.07010 1.230870 0.00000 0.390845 0.344879 0.547206 0.374467 0.307926 0.390845 0.00000 0.0000000 0.547206 0.452794 0.000000 NA NA
parent-courter_unlinked_novs_5_summary.txt_3 11999 Pop2 1000 533 467 1000 1.188380 0.465291 1.07074 1.214330 0.00000 0.403509 0.344879 0.534709 0.374307 0.303788 0.403509 0.00000 0.0000000 0.534709 0.465291 0.000000 NA NA
parent-courter_unlinked_novs_5_summary.txt_4 11999 Pop3 1000 514 486 1000 1.188380 0.463035 1.09061 1.229310 0.00000 0.489130 0.344879 0.536965 0.369337 0.307536 0.489130 0.00000 0.0000000 0.536965 0.463035 0.000000 NA NA

Multiple morphs are maintained in 20 of the 20 replicates, and those morphs contain either a parent or a courter.

Evolution of the courter and parenting trait values in each rep with unlinked genetic variation and without viability selection

Evolution of the courter and parenting trait values in each rep with unlinked genetic variation and without viability selection

Linked additive genetic variance

In these cases, the traits are encoded by a number (50) of loci, whose alleles contribute additively to determine the trait value. These alleles anchored on chromosomes, equally distributed among the chromosomes (4). The overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

With viability selection

Frequency of the courter morph with linked QTLs (each color represents a different replicate)

Frequency of the courter morph with linked QTLs (each color represents a different replicate)

When only the courtship trait is included in the simulation, 0 of the 20 replicates reached an equilibrium by 10000 generations.

This is further evidenced by looking at a table of trait values and fitnesses in the final generation of each replicate

Frequency of courters with linked QTLs in final generation
CourterFreq CourterW NonCourterW
courter_linked_1_summary.txt_1 1 1.99800 0
courter_linked_1_summary.txt_2 1 2.02439 0
courter_linked_1_summary.txt_3 1 1.96457 0
courter_linked_1_summary.txt_4 1 2.02028 0
courter_linked_2_summary.txt_1 1 1.92070 0
courter_linked_2_summary.txt_2 1 2.05350 0
courter_linked_2_summary.txt_3 1 2.00605 0
courter_linked_2_summary.txt_4 1 2.01826 0
courter_linked_3_summary.txt_1 1 1.99800 0
courter_linked_3_summary.txt_2 1 2.02439 0
courter_linked_3_summary.txt_3 1 1.96457 0
courter_linked_3_summary.txt_4 1 2.02028 0
courter_linked_4_summary.txt_1 1 2.00000 0
courter_linked_4_summary.txt_2 1 2.00401 0
courter_linked_4_summary.txt_3 1 2.02020 0
courter_linked_4_summary.txt_4 1 1.94175 0
courter_linked_5_summary.txt_1 1 2.00000 0
courter_linked_5_summary.txt_2 1 2.00401 0
courter_linked_5_summary.txt_3 1 2.02020 0
courter_linked_5_summary.txt_4 1 1.94175 0

Every rep has the courtship trait go to fixation.

Let’s also evaluate the evolution of the courtship trait values:

Evolution of courtship trait with linked loci

Evolution of courtship trait with linked loci

Without viability selection

Frequency of the courter morph with linked QTLs and no viability selection (each color represents a different replicate)

Frequency of the courter morph with linked QTLs and no viability selection (each color represents a different replicate)

When only the courtship trait is included in the simulation, 0 of the 20 replicates reached an equilibrium by 10000 generations.

This is further evidenced by looking at a table of trait values and fitnesses in the final generation of each replicate

Frequency of courters with linked QTLs in final generation
CourterFreq CourterW NonCourterW
courter_linked_novs_1_summary.txt_1 1 1.99203 0
courter_linked_novs_1_summary.txt_2 1 1.95312 0
courter_linked_novs_1_summary.txt_3 1 2.03666 0
courter_linked_novs_1_summary.txt_4 1 1.96850 0
courter_linked_novs_2_summary.txt_1 1 2.04082 0
courter_linked_novs_2_summary.txt_2 1 2.04499 0
courter_linked_novs_2_summary.txt_3 1 2.05339 0
courter_linked_novs_2_summary.txt_4 1 1.92308 0
courter_linked_novs_3_summary.txt_1 1 1.99203 0
courter_linked_novs_3_summary.txt_2 1 1.95312 0
courter_linked_novs_3_summary.txt_3 1 2.03666 0
courter_linked_novs_3_summary.txt_4 1 1.96850 0
courter_linked_novs_4_summary.txt_1 1 1.94175 0
courter_linked_novs_4_summary.txt_2 1 2.02020 0
courter_linked_novs_4_summary.txt_3 1 2.05339 0
courter_linked_novs_4_summary.txt_4 1 1.97239 0
courter_linked_novs_5_summary.txt_1 1 1.94175 0
courter_linked_novs_5_summary.txt_2 1 2.02020 0
courter_linked_novs_5_summary.txt_3 1 2.05339 0
courter_linked_novs_5_summary.txt_4 1 1.97239 0

Every rep has the courtship trait go to fixation.

Let’s also evaluate the evolution of the courtship trait values:

Evolution of courtship trait with linked loci and without viability selection

Evolution of courtship trait with linked loci and without viability selection

Parental trait

With viability selection

Frequency of parent morph with linked QTLs (each color represents a different replicate)

Frequency of parent morph with linked QTLs (each color represents a different replicate)

When only the parental trait is included in the model with linked QTLs, variable outcomes can be reached – although all include each rep reaching some stable state with minor fluctuations.

Frequency of parents with linked QTLs in final generation
ParentFreq ParentW NonParentW
parent_linked_1_summary.txt_1 0.600465 1.54780 0.443478
parent_linked_1_summary.txt_2 0.547665 1.64390 0.390805
parent_linked_1_summary.txt_3 0.526249 1.41768 0.302703
parent_linked_1_summary.txt_4 0.574138 1.57957 0.681319
parent_linked_2_summary.txt_1 0.600465 1.54780 0.443478
parent_linked_2_summary.txt_2 0.547665 1.64390 0.390805
parent_linked_2_summary.txt_3 0.526249 1.41768 0.302703
parent_linked_2_summary.txt_4 0.574138 1.57957 0.681319
parent_linked_3_summary.txt_1 0.589370 1.55238 0.424242
parent_linked_3_summary.txt_2 0.580436 1.45682 0.464286
parent_linked_3_summary.txt_3 0.579465 1.68905 0.525773
parent_linked_3_summary.txt_4 0.591772 1.50962 0.752577
parent_linked_4_summary.txt_1 0.240375 1.55125 0.710145
parent_linked_4_summary.txt_2 0.231262 1.73861 0.446429
parent_linked_4_summary.txt_3 0.234927 1.60766 0.734940
parent_linked_4_summary.txt_4 0.236218 1.57267 1.017240
parent_linked_5_summary.txt_1 0.240375 1.55125 0.710145
parent_linked_5_summary.txt_2 0.231262 1.73861 0.446429
parent_linked_5_summary.txt_3 0.234927 1.60766 0.734940
parent_linked_5_summary.txt_4 0.236218 1.57267 1.017240

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

The evolution of the trait values may shed light on the variable outcomes:

Evolution of parenting trait values with linked QTLs

Evolution of parenting trait values with linked QTLs

Without viability selection

Frequency of parent morph with linked QTLs without viability selection (each color represents a different replicate)

Frequency of parent morph with linked QTLs without viability selection (each color represents a different replicate)

When only the parental trait is included in the model with linked QTLs, variable outcomes can be reached – although all include each rep reaching some stable state with minor fluctuations.

Frequency of parents with linked QTLs in final generation, with no viability selection
ParentFreq ParentW NonParentW
parent_linked_novs_1_summary.txt_1 0.825581 1.61737 0.511111
parent_linked_novs_1_summary.txt_2 0.606000 1.62706 0.324873
parent_linked_novs_1_summary.txt_3 0.736196 1.65000 0.496124
parent_linked_novs_1_summary.txt_4 0.795082 1.60052 0.510000
parent_linked_novs_2_summary.txt_1 0.715768 1.72754 0.386861
parent_linked_novs_2_summary.txt_2 0.834264 1.51562 0.561798
parent_linked_novs_2_summary.txt_3 0.684803 1.57260 0.488095
parent_linked_novs_2_summary.txt_4 0.817269 1.55774 0.703297
parent_linked_novs_3_summary.txt_1 0.715768 1.72754 0.386861
parent_linked_novs_3_summary.txt_2 0.834264 1.51562 0.561798
parent_linked_novs_3_summary.txt_3 0.684803 1.57260 0.488095
parent_linked_novs_3_summary.txt_4 0.817269 1.55774 0.703297
parent_linked_novs_4_summary.txt_1 0.745902 1.59615 0.612903
parent_linked_novs_4_summary.txt_2 0.781250 1.71500 0.482143
parent_linked_novs_4_summary.txt_3 0.814453 1.50600 0.631579
parent_linked_novs_4_summary.txt_4 0.782435 1.61735 0.513761
parent_linked_novs_5_summary.txt_1 0.745902 1.59615 0.612903
parent_linked_novs_5_summary.txt_2 0.781250 1.71500 0.482143
parent_linked_novs_5_summary.txt_3 0.814453 1.50600 0.631579
parent_linked_novs_5_summary.txt_4 0.782435 1.61735 0.513761

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

The evolution of the trait values may shed light on the variable outcomes:

Evolution of parenting trait values with linked QTLs and without viability selection

Evolution of parenting trait values with linked QTLs and without viability selection

Courtship and Parental Traits

Including both courtship and parental traits, along with linked loci, causes the outcomes to be even less predictable.

With viability selection

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

Because of the variable outcomes, it is useful to visualize the frequencies of the four morphs with each rep in its own graph.

Frequency of the 4 morphs in each rep with linked QTLs

Frequency of the 4 morphs in each rep with linked QTLs

In some of the runs the population crashed after few generations. This is obvious both from the figures and when looking at the the final frequencies in a table as well (pay attention to the generation number column):

Frequency of morphs in final generation (linked loci)
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentAEmean ParentAEsd ParentFreq ParentW NonParentW CourterThresh CourterAEmean CourterAEsd CourterFreq CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_linked_1_summary.txt_1 11999 Pop0 1000 494 506 1000 -0.458612 0.447368 -0.4942660 0.4957500 0.0090498 0.326007 0.343049 0.376947 0.473095 0.556680 0.330909 0 0.0000000 0.552632 0.443320 0.0040486 NA NA
parent-courter_linked_1_summary.txt_2 11999 Pop1 998 507 491 1000 -0.458612 0.439842 -0.5044700 0.4945260 0.0000000 0.299296 0.343049 0.386529 0.471814 0.560158 0.299296 0 0.0000000 0.560158 0.439842 0.0000000 NA NA
parent-courter_linked_1_summary.txt_3 11999 Pop2 1000 508 492 1000 -0.458612 0.442913 -0.5021480 0.4959020 0.0000000 0.314488 0.343049 0.384785 0.473144 0.557087 0.314488 0 0.0000000 0.557087 0.442913 0.0000000 NA NA
parent-courter_linked_1_summary.txt_4 11999 Pop3 1000 484 516 1000 -0.458612 0.440083 -0.4950940 0.5009730 0.0000000 0.479705 0.343049 0.378210 0.478414 0.559917 0.479705 0 0.0000000 0.559917 0.440083 0.0000000 NA NA
parent-courter_linked_2_summary.txt_1 11999 Pop0 1000 494 506 1000 -0.458612 0.447368 -0.4942660 0.4957500 0.0090498 0.326007 0.343049 0.376947 0.473095 0.556680 0.330909 0 0.0000000 0.552632 0.443320 0.0040486 NA NA
parent-courter_linked_2_summary.txt_2 11999 Pop1 998 507 491 1000 -0.458612 0.439842 -0.5044700 0.4945260 0.0000000 0.299296 0.343049 0.386529 0.471814 0.560158 0.299296 0 0.0000000 0.560158 0.439842 0.0000000 NA NA
parent-courter_linked_2_summary.txt_3 11999 Pop2 1000 508 492 1000 -0.458612 0.442913 -0.5021480 0.4959020 0.0000000 0.314488 0.343049 0.384785 0.473144 0.557087 0.314488 0 0.0000000 0.557087 0.442913 0.0000000 NA NA
parent-courter_linked_2_summary.txt_4 11999 Pop3 1000 484 516 1000 -0.458612 0.440083 -0.4950940 0.5009730 0.0000000 0.479705 0.343049 0.378210 0.478414 0.559917 0.479705 0 0.0000000 0.559917 0.440083 0.0000000 NA NA
parent-courter_linked_3_summary.txt_1 11999 Pop0 1000 494 506 1000 -0.458612 0.447368 -0.4942660 0.4957500 0.0090498 0.326007 0.343049 0.376947 0.473095 0.556680 0.330909 0 0.0000000 0.552632 0.443320 0.0040486 NA NA
parent-courter_linked_3_summary.txt_2 11999 Pop1 998 507 491 1000 -0.458612 0.439842 -0.5044700 0.4945260 0.0000000 0.299296 0.343049 0.386529 0.471814 0.560158 0.299296 0 0.0000000 0.560158 0.439842 0.0000000 NA NA
parent-courter_linked_3_summary.txt_3 11999 Pop2 1000 508 492 1000 -0.458612 0.442913 -0.5021480 0.4959020 0.0000000 0.314488 0.343049 0.384785 0.473144 0.557087 0.314488 0 0.0000000 0.557087 0.442913 0.0000000 NA NA
parent-courter_linked_3_summary.txt_4 11999 Pop3 1000 484 516 1000 -0.458612 0.440083 -0.4950940 0.5009730 0.0000000 0.479705 0.343049 0.378210 0.478414 0.559917 0.479705 0 0.0000000 0.559917 0.440083 0.0000000 NA NA
parent-courter_linked_4_summary.txt_1 2042 Pop0 147 69 78 209 0.140770 0.231884 0.1033710 0.0523604 0.0000000 0.509434 -1.438140 -1.214650 0.311778 0.768116 0.509434 0 0.0000000 0.768116 0.231884 0.0000000 NA NA
parent-courter_linked_4_summary.txt_2 2041 Pop1 4 3 1 4 0.140770 0.000000 0.0604539 0.0803165 0.0000000 1.333330 -1.438140 -0.975535 0.462605 1.000000 1.333330 0 0.0000000 1.000000 0.000000 0.0000000 NA NA
parent-courter_linked_4_summary.txt_3 2041 Pop2 151 77 74 194 0.140770 0.363636 0.1098850 0.0542629 0.0000000 0.408163 -1.438140 -1.260750 0.311511 0.636364 0.408163 0 0.0000000 0.636364 0.363636 0.0000000 NA NA
parent-courter_linked_4_summary.txt_4 2041 Pop3 149 76 73 182 0.140770 0.421053 0.1260010 0.0376265 0.1250000 0.568182 -1.438140 -1.345830 0.215691 0.605263 0.630435 0 0.0131579 0.565789 0.381579 0.0394737 NA NA
parent-courter_linked_5_summary.txt_1 2042 Pop0 147 69 78 209 0.140770 0.231884 0.1033710 0.0523604 0.0000000 0.509434 -1.438140 -1.214650 0.311778 0.768116 0.509434 0 0.0000000 0.768116 0.231884 0.0000000 NA NA
parent-courter_linked_5_summary.txt_2 2041 Pop1 4 3 1 4 0.140770 0.000000 0.0604539 0.0803165 0.0000000 1.333330 -1.438140 -0.975535 0.462605 1.000000 1.333330 0 0.0000000 1.000000 0.000000 0.0000000 NA NA
parent-courter_linked_5_summary.txt_3 2041 Pop2 151 77 74 194 0.140770 0.363636 0.1098850 0.0542629 0.0000000 0.408163 -1.438140 -1.260750 0.311511 0.636364 0.408163 0 0.0000000 0.636364 0.363636 0.0000000 NA NA
parent-courter_linked_5_summary.txt_4 2041 Pop3 149 76 73 182 0.140770 0.421053 0.1260010 0.0376265 0.1250000 0.568182 -1.438140 -1.345830 0.215691 0.605263 0.630435 0 0.0131579 0.565789 0.381579 0.0394737 NA NA

Multiple morphs are maintained in 0 of the 20 replicates, and those morphs contain either a parent or a courter. However, 8 of those reps with variation actually crashed.

Looking at the trait value evolution may help us understand why some of the runs resulted in extinction:

Evolution of the courter and parenting trait values in each rep with linked genetic variation

Evolution of the courter and parenting trait values in each rep with linked genetic variation

Without viability selection

Frequency of the two morphs with linked QTLs and without viability selection (courter = green, parent = blue)

Frequency of the two morphs with linked QTLs and without viability selection (courter = green, parent = blue)

Because of the variable outcomes, it is useful to visualize the frequencies of the four morphs with each rep in its own graph.

Frequency of the 4 morphs in each rep with linked QTLs without viability selection

Frequency of the 4 morphs in each rep with linked QTLs without viability selection

In some of the runs the population crashed after few generations. This is obvious both from the figures and when looking at the the final frequencies in a table as well (pay attention to the generation number column):

Frequency of morphs in final generation (linked loci, no viability selection)
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentFreq ParentAEmean ParentAEsd ParentW NonParentW CourterThresh CourterFreq CourterAEmean CourterAEsd CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_linked_novs_1_summary.txt_1 11999 Pop0 1000 480 520 1000 0.933615 0.897917 1.333910 0.579584 1.9373500 1.306120 -0.114728 0.893750 0.182179 0.4312150 1.967370 1.078430 0.0895833 0.0125000 0.0166667 0.8812500 NA NA
parent-courter_linked_novs_1_summary.txt_2 11999 Pop1 993 499 494 1000 0.933615 0.885772 1.314860 0.563536 1.8936700 1.140350 -0.114728 0.887776 0.160480 0.4118220 1.896160 1.107140 0.1042080 0.0100200 0.0080160 0.8777560 NA NA
parent-courter_linked_novs_1_summary.txt_3 11999 Pop2 989 461 528 1000 0.933615 0.893709 1.335020 0.576297 2.0048500 1.367350 -0.114728 0.908894 0.191017 0.4312860 1.983290 1.476190 0.0867679 0.0195228 0.0043384 0.8893710 NA NA
parent-courter_linked_novs_1_summary.txt_4 11999 Pop3 993 513 480 1000 0.933615 0.851852 1.265330 0.522345 1.7597300 1.092110 -0.114728 0.867446 0.137293 0.3860480 1.759550 1.014710 0.1130600 0.0350877 0.0194932 0.8323590 NA NA
parent-courter_linked_novs_2_summary.txt_1 11999 Pop0 1000 493 507 1000 0.933615 0.920892 1.397390 0.621610 1.8281900 1.282050 -0.114728 0.920892 0.218400 0.4506270 1.848020 1.051280 0.0669371 0.0121704 0.0121704 0.9087220 NA NA
parent-courter_linked_novs_2_summary.txt_2 11999 Pop1 1000 526 474 1000 0.933615 0.910646 1.342900 0.567567 1.7411300 1.191490 -0.114728 0.927757 0.215363 0.4381490 1.739750 1.078950 0.0665399 0.0228137 0.0057034 0.9049430 NA NA
parent-courter_linked_novs_2_summary.txt_3 11999 Pop2 1000 506 494 1000 0.933615 0.899209 1.353970 0.582419 1.7868100 0.686275 -0.114728 0.909091 0.189434 0.4227330 1.776090 0.673913 0.0849802 0.0158103 0.0059288 0.8932810 NA NA
parent-courter_linked_novs_2_summary.txt_4 11999 Pop3 1000 467 533 1000 0.933615 0.877944 1.347710 0.617913 1.9902400 1.333330 -0.114728 0.890792 0.179219 0.4437650 1.978370 1.352940 0.1049250 0.0171306 0.0042827 0.8736620 NA NA
parent-courter_linked_novs_3_summary.txt_1 11999 Pop0 1000 493 507 1000 0.933615 0.920892 1.397390 0.621610 1.8281900 1.282050 -0.114728 0.920892 0.218400 0.4506270 1.848020 1.051280 0.0669371 0.0121704 0.0121704 0.9087220 NA NA
parent-courter_linked_novs_3_summary.txt_2 11999 Pop1 1000 526 474 1000 0.933615 0.910646 1.342900 0.567567 1.7411300 1.191490 -0.114728 0.927757 0.215363 0.4381490 1.739750 1.078950 0.0665399 0.0228137 0.0057034 0.9049430 NA NA
parent-courter_linked_novs_3_summary.txt_3 11999 Pop2 1000 506 494 1000 0.933615 0.899209 1.353970 0.582419 1.7868100 0.686275 -0.114728 0.909091 0.189434 0.4227330 1.776090 0.673913 0.0849802 0.0158103 0.0059288 0.8932810 NA NA
parent-courter_linked_novs_3_summary.txt_4 11999 Pop3 1000 467 533 1000 0.933615 0.877944 1.347710 0.617913 1.9902400 1.333330 -0.114728 0.890792 0.179219 0.4437650 1.978370 1.352940 0.1049250 0.0171306 0.0042827 0.8736620 NA NA
parent-courter_linked_novs_4_summary.txt_1 11999 Pop0 980 512 468 1000 -0.105665 0.464844 -0.114794 0.108740 0.0294118 0.412409 -0.359170 0.537109 -0.356093 0.0364008 0.436364 0.000000 0.0019531 0.5332030 0.4609380 0.0039062 NA NA
parent-courter_linked_novs_4_summary.txt_2 11999 Pop1 980 499 481 1000 -0.105665 0.464930 -0.112029 0.107393 0.0000000 0.453184 -0.359170 0.535070 -0.356999 0.0359518 0.453184 0.000000 0.0000000 0.5350700 0.4649300 0.0000000 NA NA
parent-courter_linked_novs_4_summary.txt_3 11999 Pop2 979 504 475 1000 -0.105665 0.462302 -0.114977 0.109187 0.0000000 0.372694 -0.359170 0.535714 -0.356055 0.0365506 0.374074 0.000000 0.0019841 0.5357140 0.4623020 0.0000000 NA NA
parent-courter_linked_novs_4_summary.txt_4 11999 Pop3 983 515 468 1000 -0.105665 0.454369 -0.116693 0.108979 0.0000000 0.327402 -0.359170 0.545631 -0.355486 0.0364892 0.327402 0.000000 0.0000000 0.5456310 0.4543690 0.0000000 NA NA
parent-courter_linked_novs_5_summary.txt_1 11999 Pop0 980 512 468 1000 -0.105665 0.464844 -0.114794 0.108740 0.0294118 0.412409 -0.359170 0.537109 -0.356093 0.0364008 0.436364 0.000000 0.0019531 0.5332030 0.4609380 0.0039062 NA NA
parent-courter_linked_novs_5_summary.txt_2 11999 Pop1 980 499 481 1000 -0.105665 0.464930 -0.112029 0.107393 0.0000000 0.453184 -0.359170 0.535070 -0.356999 0.0359518 0.453184 0.000000 0.0000000 0.5350700 0.4649300 0.0000000 NA NA
parent-courter_linked_novs_5_summary.txt_3 11999 Pop2 979 504 475 1000 -0.105665 0.462302 -0.114977 0.109187 0.0000000 0.372694 -0.359170 0.535714 -0.356055 0.0365506 0.374074 0.000000 0.0019841 0.5357140 0.4623020 0.0000000 NA NA
parent-courter_linked_novs_5_summary.txt_4 11999 Pop3 983 515 468 1000 -0.105665 0.454369 -0.116693 0.108979 0.0000000 0.327402 -0.359170 0.545631 -0.355486 0.0364892 0.327402 0.000000 0.0000000 0.5456310 0.4543690 0.0000000 NA NA

Multiple morphs are maintained in 20 of the 20 replicates, and those morphs contain either a parent or a courter. However, 0 of those reps with variation actually crashed.

Looking at the trait value evolution may help us understand why some of the runs resulted in extinction:

Evolution of the courter and parenting trait values in each rep with linked genetic variation and no viability selection

Evolution of the courter and parenting trait values in each rep with linked genetic variation and no viability selection

Supergenes

In these cases, the loci (50) are all located in one region of a chromosome, and that region has reduced recombination. As above, the overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

With viability selection

Frequency of the courter morph with supergenes (each color represents a different replicate)

Frequency of the courter morph with supergenes (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters with supergenes in final generation
CourterFreq CourterW NonCourterW
courter_supergene_1_summary.txt_1 1 1.89394 0
courter_supergene_1_summary.txt_2 1 2.08768 0
courter_supergene_1_summary.txt_3 1 2.03252 0
courter_supergene_1_summary.txt_4 1 2.01613 0
courter_supergene_2_summary.txt_1 1 1.96078 0
courter_supergene_2_summary.txt_2 1 2.00803 0
courter_supergene_2_summary.txt_3 1 2.03666 0
courter_supergene_2_summary.txt_4 1 1.98807 0
courter_supergene_3_summary.txt_1 1 1.89394 0
courter_supergene_3_summary.txt_2 1 2.08768 0
courter_supergene_3_summary.txt_3 1 2.03252 0
courter_supergene_3_summary.txt_4 1 2.01613 0
courter_supergene_4_summary.txt_1 1 2.03265 0
courter_supergene_4_summary.txt_2 1 2.12848 0
courter_supergene_4_summary.txt_3 1 2.04517 0
courter_supergene_4_summary.txt_4 1 2.02240 0
courter_supergene_5_summary.txt_1 1 2.03265 0
courter_supergene_5_summary.txt_2 1 2.12848 0
courter_supergene_5_summary.txt_3 1 2.04517 0
courter_supergene_5_summary.txt_4 1 2.02240 0

Looking at the evolution of the trait values:

Evolution of courtship trait with a supergene

Evolution of courtship trait with a supergene

Without viability selection

Frequency of the courter morph with supergenes without viability selection (each color represents a different replicate)

Frequency of the courter morph with supergenes without viability selection (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters with supergenes in final generation with no viability selection
CourterFreq CourterW NonCourterW
courter_supergene_novs_1_summary.txt_1 1 2.06186 0
courter_supergene_novs_1_summary.txt_2 1 1.94553 0
courter_supergene_novs_1_summary.txt_3 1 1.93424 0
courter_supergene_novs_1_summary.txt_4 1 1.99601 0
courter_supergene_novs_2_summary.txt_1 1 2.06186 0
courter_supergene_novs_2_summary.txt_2 1 1.94553 0
courter_supergene_novs_2_summary.txt_3 1 1.93424 0
courter_supergene_novs_2_summary.txt_4 1 1.99601 0
courter_supergene_novs_3_summary.txt_1 1 1.93798 0
courter_supergene_novs_3_summary.txt_2 1 1.98807 0
courter_supergene_novs_3_summary.txt_3 1 1.96078 0
courter_supergene_novs_3_summary.txt_4 1 2.00000 0
courter_supergene_novs_4_summary.txt_1 1 2.02429 0
courter_supergene_novs_4_summary.txt_2 1 2.07469 0
courter_supergene_novs_4_summary.txt_3 1 2.07469 0
courter_supergene_novs_4_summary.txt_4 1 2.04499 0
courter_supergene_novs_5_summary.txt_1 1 2.02429 0
courter_supergene_novs_5_summary.txt_2 1 2.07469 0
courter_supergene_novs_5_summary.txt_3 1 2.07469 0
courter_supergene_novs_5_summary.txt_4 1 2.04499 0

Looking at the evolution of the trait values:

Evolution of courtship trait with a supergene and without viability selection

Evolution of courtship trait with a supergene and without viability selection

Parental trait

With viability selection

Frequency of parent morph with supergenes (each color represents a different replicate)

Frequency of parent morph with supergenes (each color represents a different replicate)

Frequency of parents with supergenes in final generation
ParentFreq ParentW NonParentW
parent_supergene_1_summary.txt_1 1.1443500 1.46189 0.670000
parent_supergene_1_summary.txt_2 1.1917500 1.56757 0.826087
parent_supergene_1_summary.txt_3 1.1563500 1.65963 0.628319
parent_supergene_1_summary.txt_4 1.1744700 1.55932 0.682927
parent_supergene_2_summary.txt_1 1.1443500 1.46189 0.670000
parent_supergene_2_summary.txt_2 1.1917500 1.56757 0.826087
parent_supergene_2_summary.txt_3 1.1563500 1.65963 0.628319
parent_supergene_2_summary.txt_4 1.1744700 1.55932 0.682927
parent_supergene_3_summary.txt_1 0.0415676 1.71264 0.492308
parent_supergene_3_summary.txt_2 0.0403339 1.63820 0.441176
parent_supergene_3_summary.txt_3 0.0401651 1.77017 0.710526
parent_supergene_3_summary.txt_4 0.0404482 1.65455 0.691176
parent_supergene_4_summary.txt_1 0.0415676 1.71264 0.492308
parent_supergene_4_summary.txt_2 0.0403339 1.63820 0.441176
parent_supergene_4_summary.txt_3 0.0401651 1.77017 0.710526
parent_supergene_4_summary.txt_4 0.0404482 1.65455 0.691176
parent_supergene_5_summary.txt_1 0.0415676 1.71264 0.492308
parent_supergene_5_summary.txt_2 0.0403339 1.63820 0.441176
parent_supergene_5_summary.txt_3 0.0401651 1.77017 0.710526
parent_supergene_5_summary.txt_4 0.0404482 1.65455 0.691176

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Let’s look at the trajectories of the parent traits.

Evolution of parenting trait values with a supergene

Evolution of parenting trait values with a supergene

Without viability selection

Frequency of parent morph with supergenes without viability selection (each color represents a different replicate)

Frequency of parent morph with supergenes without viability selection (each color represents a different replicate)

Frequency of parents with supergenes in final generation without viability selection
ParentFreq ParentW NonParentW
parent_supergene_novs_1_summary.txt_1 0.881092 1.62611 0.557377
parent_supergene_novs_1_summary.txt_2 0.868726 1.70000 0.558824
parent_supergene_novs_1_summary.txt_3 0.855131 1.62824 0.486111
parent_supergene_novs_1_summary.txt_4 0.875740 1.62162 0.761905
parent_supergene_novs_2_summary.txt_1 0.866142 1.71136 0.779412
parent_supergene_novs_2_summary.txt_2 0.875264 1.86473 0.864407
parent_supergene_novs_2_summary.txt_3 0.851301 1.53493 0.512500
parent_supergene_novs_2_summary.txt_4 0.862786 1.77108 0.560606
parent_supergene_novs_3_summary.txt_1 0.860153 1.55679 0.753425
parent_supergene_novs_3_summary.txt_2 0.871743 1.69885 0.750000
parent_supergene_novs_3_summary.txt_3 0.835317 1.53682 0.759036
parent_supergene_novs_3_summary.txt_4 0.835968 1.62411 0.590361
parent_supergene_novs_4_summary.txt_1 0.860153 1.55679 0.753425
parent_supergene_novs_4_summary.txt_2 0.871743 1.69885 0.750000
parent_supergene_novs_4_summary.txt_3 0.835317 1.53682 0.759036
parent_supergene_novs_4_summary.txt_4 0.835968 1.62411 0.590361
parent_supergene_novs_5_summary.txt_1 0.860153 1.55679 0.753425
parent_supergene_novs_5_summary.txt_2 0.871743 1.69885 0.750000
parent_supergene_novs_5_summary.txt_3 0.835317 1.53682 0.759036
parent_supergene_novs_5_summary.txt_4 0.835968 1.62411 0.590361

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Let’s look at the trajectories of the parent traits.

Evolution of parenting trait values with a supergene without viability selection

Evolution of parenting trait values with a supergene without viability selection

Courtship and Parental Traits

With viability selection

The different runs have different outcomes. To better see this, let’s look at the morph frequencies in each rep separately.

Frequency of the 4 morphs in each rep with supergenes

Frequency of the 4 morphs in each rep with supergenes

Frequency of morphs in final generation (supergenes)
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentAEmean ParentAEsd ParentFreq ParentW NonParentW CourterThresh CourterAEmean CourterAEsd CourterFreq CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_supergene_1_summary.txt_1 11999 Pop0 943 472 471 1000 0.890749 0.442797 0.881010 0.0753190 0 0.414449 -0.942183 -0.795600 1.133670 0.557203 0.414449 0 0 0.557203 0.442797 0 NA NA
parent-courter_supergene_1_summary.txt_2 11999 Pop1 944 482 462 1000 0.890749 0.429461 0.881584 0.0739243 0 0.305455 -0.942183 -0.804237 1.112670 0.570539 0.305455 0 0 0.570539 0.429461 0 NA NA
parent-courter_supergene_1_summary.txt_3 11999 Pop2 939 471 468 1000 0.890749 0.456476 0.886884 0.0729530 0 0.312500 -0.942183 -0.884011 1.098050 0.543524 0.312500 0 0 0.543524 0.456476 0 NA NA
parent-courter_supergene_1_summary.txt_4 11999 Pop3 939 479 460 1000 0.890749 0.430063 0.882684 0.0733204 0 0.391941 -0.942183 -0.820793 1.103580 0.569937 0.391941 0 0 0.569937 0.430063 0 NA NA
parent-courter_supergene_2_summary.txt_1 11999 Pop0 943 472 471 1000 0.890749 0.442797 0.881010 0.0753190 0 0.414449 -0.942183 -0.795600 1.133670 0.557203 0.414449 0 0 0.557203 0.442797 0 NA NA
parent-courter_supergene_2_summary.txt_2 11999 Pop1 944 482 462 1000 0.890749 0.429461 0.881584 0.0739243 0 0.305455 -0.942183 -0.804237 1.112670 0.570539 0.305455 0 0 0.570539 0.429461 0 NA NA
parent-courter_supergene_2_summary.txt_3 11999 Pop2 939 471 468 1000 0.890749 0.456476 0.886884 0.0729530 0 0.312500 -0.942183 -0.884011 1.098050 0.543524 0.312500 0 0 0.543524 0.456476 0 NA NA
parent-courter_supergene_2_summary.txt_4 11999 Pop3 939 479 460 1000 0.890749 0.430063 0.882684 0.0733204 0 0.391941 -0.942183 -0.820793 1.103580 0.569937 0.391941 0 0 0.569937 0.430063 0 NA NA
parent-courter_supergene_3_summary.txt_1 11999 Pop0 916 439 477 1000 -0.396641 0.412301 -0.454427 0.5549950 0 0.426357 -0.383509 -0.325517 0.556975 0.587699 0.426357 0 0 0.587699 0.412301 0 NA NA
parent-courter_supergene_3_summary.txt_2 11999 Pop1 959 464 495 1000 -0.396641 0.418103 -0.445153 0.5536360 0 0.362963 -0.383509 -0.334824 0.555611 0.581897 0.362963 0 0 0.581897 0.418103 0 NA NA
parent-courter_supergene_3_summary.txt_3 11999 Pop2 939 454 485 1000 -0.396641 0.411894 -0.442378 0.5484150 0 0.486891 -0.383509 -0.337609 0.550371 0.588106 0.486891 0 0 0.588106 0.411894 0 NA NA
parent-courter_supergene_3_summary.txt_4 11999 Pop3 955 469 486 1000 -0.396641 0.424307 -0.434795 0.5519460 0 0.292593 -0.383509 -0.345219 0.553915 0.575693 0.292593 0 0 0.575693 0.424307 0 NA NA
parent-courter_supergene_4_summary.txt_1 11999 Pop0 916 439 477 1000 -0.396641 0.412301 -0.454427 0.5549950 0 0.426357 -0.383509 -0.325517 0.556975 0.587699 0.426357 0 0 0.587699 0.412301 0 NA NA
parent-courter_supergene_4_summary.txt_2 11999 Pop1 959 464 495 1000 -0.396641 0.418103 -0.445153 0.5536360 0 0.362963 -0.383509 -0.334824 0.555611 0.581897 0.362963 0 0 0.581897 0.418103 0 NA NA
parent-courter_supergene_4_summary.txt_3 11999 Pop2 939 454 485 1000 -0.396641 0.411894 -0.442378 0.5484150 0 0.486891 -0.383509 -0.337609 0.550371 0.588106 0.486891 0 0 0.588106 0.411894 0 NA NA
parent-courter_supergene_4_summary.txt_4 11999 Pop3 955 469 486 1000 -0.396641 0.424307 -0.434795 0.5519460 0 0.292593 -0.383509 -0.345219 0.553915 0.575693 0.292593 0 0 0.575693 0.424307 0 NA NA
parent-courter_supergene_5_summary.txt_1 11999 Pop0 916 439 477 1000 -0.396641 0.412301 -0.454427 0.5549950 0 0.426357 -0.383509 -0.325517 0.556975 0.587699 0.426357 0 0 0.587699 0.412301 0 NA NA
parent-courter_supergene_5_summary.txt_2 11999 Pop1 959 464 495 1000 -0.396641 0.418103 -0.445153 0.5536360 0 0.362963 -0.383509 -0.334824 0.555611 0.581897 0.362963 0 0 0.581897 0.418103 0 NA NA
parent-courter_supergene_5_summary.txt_3 11999 Pop2 939 454 485 1000 -0.396641 0.411894 -0.442378 0.5484150 0 0.486891 -0.383509 -0.337609 0.550371 0.588106 0.486891 0 0 0.588106 0.411894 0 NA NA
parent-courter_supergene_5_summary.txt_4 11999 Pop3 955 469 486 1000 -0.396641 0.424307 -0.434795 0.5519460 0 0.292593 -0.383509 -0.345219 0.553915 0.575693 0.292593 0 0 0.575693 0.424307 0 NA NA

Multiple morphs are maintained in 0 of the 20 replicates, and those morphs contain either a parent or a courter. 0 of those reps with variation went extinct before 10000 generations.

Evolution of the courter and parenting trait values in each rep with a supergene

Evolution of the courter and parenting trait values in each rep with a supergene

Without viability selection

The different runs have different outcomes. To better see this, let’s look at the morph frequencies in each rep separately.

Frequency of the 4 morphs in each rep with supergenes without viability selection

Frequency of the 4 morphs in each rep with supergenes without viability selection

Frequency of morphs in final generation (supergenes and no viability selection)
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentFreq ParentAEmean ParentAEsd ParentW NonParentW CourterThresh CourterFreq CourterAEmean CourterAEsd CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_supergene_novs_1_summary.txt_1 11999 Pop0 1000 539 461 1000 -0.125284 0.411874 -0.221956 0.8489540 0.00000 0.198738 0.854845 0.588126 0.883836 0.254588 0.198738 0.00000 0.0000000 0.588126 0.411874 0.000000 NA NA
parent-courter_supergene_novs_1_summary.txt_2 11999 Pop1 1000 540 460 1000 -0.125284 0.416667 -0.225065 0.8549870 0.00000 0.257143 0.854845 0.583333 0.884768 0.256397 0.257143 0.00000 0.0000000 0.583333 0.416667 0.000000 NA NA
parent-courter_supergene_novs_1_summary.txt_3 11999 Pop2 1000 536 464 1000 -0.125284 0.421642 -0.212558 0.8529190 0.00000 0.267742 0.854845 0.578358 0.881017 0.255777 0.267742 0.00000 0.0000000 0.578358 0.421642 0.000000 NA NA
parent-courter_supergene_novs_1_summary.txt_4 11999 Pop3 1000 536 464 1000 -0.125284 0.421642 -0.199379 0.8459160 0.00000 0.293548 0.854845 0.578358 0.877065 0.253677 0.293548 0.00000 0.0000000 0.578358 0.421642 0.000000 NA NA
parent-courter_supergene_novs_2_summary.txt_1 11999 Pop0 1000 539 461 1000 -0.125284 0.411874 -0.221956 0.8489540 0.00000 0.198738 0.854845 0.588126 0.883836 0.254588 0.198738 0.00000 0.0000000 0.588126 0.411874 0.000000 NA NA
parent-courter_supergene_novs_2_summary.txt_2 11999 Pop1 1000 540 460 1000 -0.125284 0.416667 -0.225065 0.8549870 0.00000 0.257143 0.854845 0.583333 0.884768 0.256397 0.257143 0.00000 0.0000000 0.583333 0.416667 0.000000 NA NA
parent-courter_supergene_novs_2_summary.txt_3 11999 Pop2 1000 536 464 1000 -0.125284 0.421642 -0.212558 0.8529190 0.00000 0.267742 0.854845 0.578358 0.881017 0.255777 0.267742 0.00000 0.0000000 0.578358 0.421642 0.000000 NA NA
parent-courter_supergene_novs_2_summary.txt_4 11999 Pop3 1000 536 464 1000 -0.125284 0.421642 -0.199379 0.8459160 0.00000 0.293548 0.854845 0.578358 0.877065 0.253677 0.293548 0.00000 0.0000000 0.578358 0.421642 0.000000 NA NA
parent-courter_supergene_novs_3_summary.txt_1 11999 Pop0 944 478 466 1000 -0.300758 0.912134 -0.226742 0.0783806 1.93349 1.119050 1.482630 0.912134 2.460770 1.035820 1.933490 1.11905 0.0878661 0.000000 0.000000 0.912134 NA NA
parent-courter_supergene_novs_3_summary.txt_2 11999 Pop1 945 458 487 1000 -0.300758 0.927948 -0.225552 0.0791775 2.03529 1.878790 1.482630 0.927948 2.476500 1.046350 2.035290 1.87879 0.0720524 0.000000 0.000000 0.927948 NA NA
parent-courter_supergene_novs_3_summary.txt_3 11999 Pop2 1000 476 524 1000 -0.300758 0.888655 -0.230285 0.0783230 2.00000 1.018870 1.482630 0.888655 2.413950 1.035060 2.000000 1.01887 0.1113450 0.000000 0.000000 0.888655 NA NA
parent-courter_supergene_novs_3_summary.txt_4 11999 Pop3 974 465 509 1000 -0.300758 0.909677 -0.227153 0.0783998 1.96454 1.547620 1.482630 0.909677 2.455350 1.036080 1.964540 1.54762 0.0903226 0.000000 0.000000 0.909677 NA NA
parent-courter_supergene_novs_4_summary.txt_1 11999 Pop0 944 478 466 1000 -0.300758 0.912134 -0.226742 0.0783806 1.93349 1.119050 1.482630 0.912134 2.460770 1.035820 1.933490 1.11905 0.0878661 0.000000 0.000000 0.912134 NA NA
parent-courter_supergene_novs_4_summary.txt_2 11999 Pop1 945 458 487 1000 -0.300758 0.927948 -0.225552 0.0791775 2.03529 1.878790 1.482630 0.927948 2.476500 1.046350 2.035290 1.87879 0.0720524 0.000000 0.000000 0.927948 NA NA
parent-courter_supergene_novs_4_summary.txt_3 11999 Pop2 1000 476 524 1000 -0.300758 0.888655 -0.230285 0.0783230 2.00000 1.018870 1.482630 0.888655 2.413950 1.035060 2.000000 1.01887 0.1113450 0.000000 0.000000 0.888655 NA NA
parent-courter_supergene_novs_4_summary.txt_4 11999 Pop3 974 465 509 1000 -0.300758 0.909677 -0.227153 0.0783998 1.96454 1.547620 1.482630 0.909677 2.455350 1.036080 1.964540 1.54762 0.0903226 0.000000 0.000000 0.909677 NA NA
parent-courter_supergene_novs_5_summary.txt_1 11999 Pop0 944 478 466 1000 -0.300758 0.912134 -0.226742 0.0783806 1.93349 1.119050 1.482630 0.912134 2.460770 1.035820 1.933490 1.11905 0.0878661 0.000000 0.000000 0.912134 NA NA
parent-courter_supergene_novs_5_summary.txt_2 11999 Pop1 945 458 487 1000 -0.300758 0.927948 -0.225552 0.0791775 2.03529 1.878790 1.482630 0.927948 2.476500 1.046350 2.035290 1.87879 0.0720524 0.000000 0.000000 0.927948 NA NA
parent-courter_supergene_novs_5_summary.txt_3 11999 Pop2 1000 476 524 1000 -0.300758 0.888655 -0.230285 0.0783230 2.00000 1.018870 1.482630 0.888655 2.413950 1.035060 2.000000 1.01887 0.1113450 0.000000 0.000000 0.888655 NA NA
parent-courter_supergene_novs_5_summary.txt_4 11999 Pop3 974 465 509 1000 -0.300758 0.909677 -0.227153 0.0783998 1.96454 1.547620 1.482630 0.909677 2.455350 1.036080 1.964540 1.54762 0.0903226 0.000000 0.000000 0.909677 NA NA

Multiple morphs are maintained in 20 of the 20 replicates, and those morphs contain either a parent or a courter. 0 of those reps with variation went extinct before 10000 generations.

Evolution of the courter and parenting trait values in each rep with a supergene without viability selection

Evolution of the courter and parenting trait values in each rep with a supergene without viability selection